Fast and Flexible Probabilistic Model Counting.

We present a probabilistic model counter that can trade off running time with approximation accuracy. As in several previous works, the number of models of a formula is estimated by adding random parity constraints (equations). One key difference with prior works is that the systems of parity equations used correspond to the parity check matrices of Low Density Parity Check (LDPC) error-correcting codes. As a result, the equations tend to be much shorter, often containing fewer than 10 variables each, making the search for models that also satisfy the parity constraints far more tractable. The price paid for computational tractability is that the statistical properties of the basic estimator are not as good as when longer constraints are used. We show how one can deal with this issue and derive rigorous approximation guarantees by performing more solver invocations.